Compact closed class of graphs

Compact closed class of graphs --- компактно замкнутый класс графов.

A class [math]\displaystyle{ {\mathcal C} }[/math] of graphs is said to be compact closed if, whenever a graph [math]\displaystyle{ G }[/math] is such that each of its finite subgraphs is contained in a finite induced subgraph of [math]\displaystyle{ G }[/math] which belongs to the class [math]\displaystyle{ {\mathcal C} }[/math], the graph [math]\displaystyle{ G }[/math] itself belongs to [math]\displaystyle{ {\mathcal C} }[/math]. We will say that a class [math]\displaystyle{ {\mathcal C} }[/math] of graphs is dually compact closed if, for every infinite [math]\displaystyle{ G \in {\mathcal C} }[/math], each finite subgraph of [math]\displaystyle{ G }[/math] is contained in a finite induced subgraph of [math]\displaystyle{ G }[/math] which belongs to [math]\displaystyle{ {\mathcal C} }[/math].